If the camers takes pictures but the LCD remains lack - this us usually a back light failure
[In which case you should see shadow images] or a connector is off whereby you see nothing.
Nothing for you to do here except to get onto Sony customer support - where I suspect if the camera is more than a year old you will be looking at the price of a new camera.

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From what I can understand, if the camera is sill able take pictures but is not displaying any thing on the LCD, then it is a problem with the LCD or LCD cable connecting to rest of the camera or LCD driver on main board.

I've had the same problem for a while now too.The camera has been useless and Im looking to replace it.Im sure this problem hasnt got a simple fix and im better off buying a new camera!Id like to here if someone managed to get it fixed thou ?

It sounds like a bad connection on the ribbon cable of the LCD screen to the camera's motherboard. The fact that when you physically move the camera around and you can get the screen to then work, tells me something is loose inside.

If you are able to see the picture in the LCD in black color and if there are no damages to the LCD -the LCD is fine.
There is a back light panel attached behind the LCD which may be defective.Check for the loose connections.
If you need spare parts contact me.

No I don't believe it is your shutter, more than likely it is a LCD Screen problem. I would suggest you take your camera back to the shop where you purchased the camera and have it serviced under warranty.
I had a customer with an Optio 550 come in and it looked like every shot was taken through 'venetian blinds' and the problem was with the LCD Screen and the camera was sent back to Pentax and repaired under warranty.